The goal of this section is to study various types of nilpotency, recently introduced in [1]}, for the left semi-braces characterized in Section 2. In particular, we characterize the ones that are right nilpotent and we find sufficient conditions to be right nil or left nil. These results will be applied to partially understand left and right nilpotency of the left semi-braces of size \(pq\)  and \(2p^2\)  obtained in Sections 3 and 4, many of which will allow us to answer in negative to [1]}.
